If `z=3-5i`, then show that `z^(3)-10z^(2)+58z-136=0`

If z=2-3i, then show that z^(2)-4z+13=0 .

If |z-3|=3, then show that (z-6)/(z)=i tan(arg z)

If |z-3|=3, then show that (z-6)/(z)=i tan(arg z)

If z=3+5i, then z^(3)+z+198

If z = 3 + 2i , prove that z^(2) - 6z + 13 = 0 and hence deduce that 3z^(3) - 13z^(2) + 9z + 65 = 0 .

If z=3+5i, then z^(3)+z+198=

If z=2-3i show that z^(2)-4z+13=0 and hence find the value of 4z^(3)-3z^(2)+169

if z_(1),z_(2),z_(3),…..z_(n) are complex numbers such that |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1 Then show that |z_(1) +z_(2) +z_(3) +……+z_(n)|=1

Show that if iz^(3)+z^(2)-z+i=0, then |z|=1